1. **State the problem:** We need to find the value of $x$ such that quadrilateral ABCD is a parallelogram. 2. **Recall the property:** In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180 degrees). Here, angles at vertices B and A are given as $3x - 6$ and $2x$ respectively. 3. **Set up the equation:** Since angles at A and B are adjacent, they must be supplementary: $$ (3x - 6) + 2x = 180 $$ 4. **Simplify the equation:** $$ 3x - 6 + 2x = 180 $$ $$ 5x - 6 = 180 $$ 5. **Solve for $x$:** Add 6 to both sides: $$ 5x - \cancel{6} + 6 = 180 + 6 $$ $$ 5x = 186 $$ Divide both sides by 5: $$ \frac{5x}{\cancel{5}} = \frac{186}{\cancel{5}} $$ $$ x = 37.2 $$ 6. **Conclusion:** The value of $x$ must be $37.2$ for ABCD to be a parallelogram.